Quality Control and Calibration of the Dual-Polarization Radar at Kwajalein, RMI

David A. Marks Laboratory for Atmospheres, NASA Goddard Space Flight Center, Greenbelt, and Science Systems and Applications, Inc., Lanham, Maryland

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David B. Wolff Laboratory for Atmospheres, NASA Goddard Space Flight Center, Greenbelt, and Science Systems and Applications, Inc., Lanham, Maryland

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Lawrence D. Carey Earth System Science Center, The University of Alabama in Huntsville, Huntsville, Alabama

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Ali Tokay Laboratory for Atmospheres, NASA Goddard Space Flight Center, Greenbelt, and Joint Center for Earth Systems Technology, University of Maryland, Baltimore County, Baltimore, Maryland

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Abstract

The dual-polarization weather radar on the Kwajalein Atoll in the Republic of the Marshall Islands (KPOL) is one of the only full-time (24/7) operational S-band dual-polarimetric (DP) radars in the tropics. Through the use of KPOL DP and disdrometer measurements from Kwajalein, quality control (QC) and reflectivity calibration techniques were developed and adapted for use. Data studies in light rain show that KPOL DP measurements are of sufficient quality for these applications. While the methodology for the development of such applications is well documented, the tuning of specific algorithms to the particular regime and observed raindrop size distributions requires a comprehensive testing and adjustment period. Presented are algorithm descriptions and results from five case studies in which QC and absolute reflectivity calibration were performed and assessed. Also described is a unique approach for calibrating the differential reflectivity field when vertically pointing observations are not available. Results show the following: 1) DP-based QC provides superior results compared to the legacy Tropical Rainfall Measuring Mission (TRMM) QC algorithm (based on height and reflectivity thresholds), and 2) absolute reflectivity calibration can be performed using observations of light rain via a published differential phase–based integration technique; results are within ±1 dB compared to independent measurements. Future extension of these algorithms to upgraded Weather Surveillance Radar-1988 Doppler (WSR-88D) polarization diverse radars will benefit National Aeronautics and Space Administration’s (NASA’s) Precipitation Measurement Missions (PMM) validation programs.

Corresponding author address: David A. Marks, Code 613.1, SSAI, NASA/GSFC, Greenbelt, MD 20771. Email: david.a.marks@nasa.gov

Abstract

The dual-polarization weather radar on the Kwajalein Atoll in the Republic of the Marshall Islands (KPOL) is one of the only full-time (24/7) operational S-band dual-polarimetric (DP) radars in the tropics. Through the use of KPOL DP and disdrometer measurements from Kwajalein, quality control (QC) and reflectivity calibration techniques were developed and adapted for use. Data studies in light rain show that KPOL DP measurements are of sufficient quality for these applications. While the methodology for the development of such applications is well documented, the tuning of specific algorithms to the particular regime and observed raindrop size distributions requires a comprehensive testing and adjustment period. Presented are algorithm descriptions and results from five case studies in which QC and absolute reflectivity calibration were performed and assessed. Also described is a unique approach for calibrating the differential reflectivity field when vertically pointing observations are not available. Results show the following: 1) DP-based QC provides superior results compared to the legacy Tropical Rainfall Measuring Mission (TRMM) QC algorithm (based on height and reflectivity thresholds), and 2) absolute reflectivity calibration can be performed using observations of light rain via a published differential phase–based integration technique; results are within ±1 dB compared to independent measurements. Future extension of these algorithms to upgraded Weather Surveillance Radar-1988 Doppler (WSR-88D) polarization diverse radars will benefit National Aeronautics and Space Administration’s (NASA’s) Precipitation Measurement Missions (PMM) validation programs.

Corresponding author address: David A. Marks, Code 613.1, SSAI, NASA/GSFC, Greenbelt, MD 20771. Email: david.a.marks@nasa.gov

1. Introduction and KPOL site description

Dual-polarimetric (DP) ground-based weather radars are well recognized as vital instruments for applications in hydrology, precipitation microphysics, and hydrometeor identification (Ryzhkov and Zrnic 1998a; Vivekanandan et al. 1999; Straka et al. 2000; Gorgucci et al. 2001; Wang and Carey 2005, among others). Supporting the U.S. Army, and the National Aeronautics and Space Administration’s (NASA’s) Tropical Rainfall Measuring Mission (TRMM) and Global Precipitation Measurement (GPM) ground validation (GV) operations at Kwajalein, Republic of the Marshall Islands (Fig. 1), an S-band DP radar (KPOL) operates on a continual basis, providing unique opportunities for algorithm development (Schumacher and Houze 2000; Houze et al. 2004; Wolff et al. 2005; Wang and Wolff 2009; Morris and Schwaller 2009).

A goal of the GPM GV program is to improve the accuracy of rainfall retrievals by developing and improving physically based radiometer algorithms for application over land and ocean. This approach requires insight into the properties of ice microphysics, parameters of local and regional drop size distributions (DSDs), and delineation between water phases. Through careful observation, DP radars can provide a means to cross-validate parameterized microphysical properties in GPM radiometer retrieval algorithms (Kummerow and Petersen 2006; Chandrasekar et al. 2008).

Kwajalein is an oceanic site, and the DP algorithms for quality control (QC), self-consistency calibration, hydrometeor identification, and rain-rate estimation provide an opportunity for the validation of microphysical properties in ocean-based radiometer retrievals from storm to climate scale. KPOL calibration is verified by two independent methods: DP self-consistency (adapted from Ryzhkov et al. 2005) and relative calibration adjustment (RCA; from Silberstein et al. 2008). As discussed in section 3, there is good agreement between the methods.

It is envisioned that DP algorithms (and possibly RCA) can be extended to Weather Surveillance Radar-1988 Doppler (WSR-88D) radar sites for GPM-related and other applied research applications. The TRMM GPM GV programs require continued verification of WSR-88D calibration and QCed data for applied research. The corrected and calibrated DP data will be of value for NASA’s Precipitation Measurement Missions (PMM) GV programs by providing observations from numerous meteorological regimes. Deployment of DP diverse WSR-88D radars is scheduled to begin in October 2010 (Istok et al. 2009), so it is relevant that preparations for the upgraded radars are considered.

This manuscript discusses the development and adaptation of DP QC and self-consistency calibration algorithms with the KPOL radar for the purpose of exploring DP-based validation capabilities. Section 2 describes the overall quality of the KPOL data as compared to established DP research radars, and details the physically based QC techniques applied to the low-level sweeps. The DP QC algorithm is tuned and applied to the lowest two elevation angles to ensure that the data are below the melting level. Section 3 provides a method for the calibration of differential reflectivity and the application of self-consistency reflectivity calibration using properties of the rainfall medium. The predominance of light rain at Kwajalein is ideal for the self-consistency calibration technique of Ryzhkov et al. (2005), wherein calculated and estimated phase data are compared to determine absolute reflectivity bias. Finally, methods and results are summarized in section 4, and considerations for extending the DP algorithms to WSR-88D radars for NASA’s PMM GV programs are discussed.

2. KPOL quality control

a. Data quality

KPOL was upgraded to DP capability in early 1998. Basic KPOL characteristics, routinely observed parameters, and scanning strategies are shown in Tables 1 and 2. Because of a litany of engineering and mechanical issues with KPOL (Houze et al. 2004; Marks et al. 2009), DP data were not reliable until 2006. To determine the basic quality of KPOL DP data, empirical comparisons were made with two established DP research radars. The National Center for Atmospheric Research (NCAR) S-band dual-polarization Doppler radar (S-Pol; Lutz et al. 1995) and the Colorado State University–University of Chicago–Illinois State Water Survey (CSU–CHILL) S-band polarimetric radar [see Brunkow et al. (2000); both of which have klystron transmitters] were used as comparison benchmarks to evaluate relative KPOL performance. This was accomplished through analysis of DP measurements in very light rain (defined as 20 dBZZH ≤ 28 dBZ, where ZH is the horizontal reflectivity component). In this context, drops are essentially spherical with little or no variability in shape, canting angle, or scattering properties within a radar resolution volume (Doviak and Zrnic 1993). Therefore, DP measurements from this medium are used as indicators of data quality.

In polarimetric radar applications, the copolar correlation coefficient (ρHV) is a measure of the correlation between horizontally and vertically polarized weather signals. It is primarily affected by the variability in the ratio of the vertical-to-horizontal size of hydrometeors in the resolution volume. Theoretical values of ρHV larger than 0.99 are indicated by Sachidananda and Zrnic (1985) because of the small shape effects in rain, but theory does not account for possible decreases resulting from sidelobes and receiver noise. Measurements in rain indicate an average ρHV of 0.98 (Doviak and Zrnic 1993) with a standard deviation of 0.01. Therefore, the significant deviation (>0.01) of ρHV below 0.98 in light rain is a likely indicator of general radar system issues.

Other values of polarimetric measurements in light rain (Doviak and Zrnic 1993, their Table 8.1) include the analysis of both specific differential phase (KDP) and differential reflectivity (ZDR), where median KDP measurements should be approximately 0° km−1, and average deviation of ZDR from its mean value [Eq. (1)] should be approximately 0 dB, that is,
i1520-0426-28-2-181-e1
where N is the number of ZDR gates within the light rain dataset. In addition, the average absolute deviation (AAD) of ZDR from its mean [Eq. (2)] provides an error measurement in ZDR that is analogous to the root-mean-square (rms) error (where N is the ZDR sample size),
i1520-0426-28-2-181-e2

DP observations in light rain were compared from the three S-band radars: CSU–CHILL, S-Pol, and KPOL. Only one volume from CSU–CHILL and S-Pol was available for comparison. Table 3 shows the median ρHV and KDP measurements (with their standard deviation), the average deviation of ZDR, and the average absolute deviation of ZDR [Eqs. (1) and (2)] for specific light rain events from the three radars under typical operating conditions. The statistical sample size from each radar was similar (∼5100 gates) and was obtained from a sector with uniform light rain. These KPOL measurements appear comparable to those from CSU–CHILL and S-Pol, and are in agreement with the previous discussion for expected observations in light rain.

To determine if KDP data are of sufficient quality for numerous applications (QC, self-consistency calibration, rain-rate estimation, and hydrometeor identification), the standard deviation of total differential phase σDP) in light rain was examined. As discussed in the literature, a reasonable range for σDP) should be approximately 2°–3° or lower for KDP-based applications (for review, e.g., see Doviak and Zrnic 1993; Bringi and Chandrasekar 2001). The standard deviation was computed at each range gate from a running, centered 25-gate sample in the radial direction (21-gate sample from CSU–CHILL and S-Pol). This corresponds with 0.2-km gate spacing and the SIGMET RVP8 processor KDP length scale of 5 km. Again, with a similar sample size, the KPOL observations are in good agreement with the other radars (Table 3) and show σDP) ≈ 2.5° with a dispersion of 0.6°. The relatively higher value for KPOL σDP) (compared to CSU–CHILL and S-Pol) is within acceptable boundaries for the development of KDP-based applications. Statistics from 12 KPOL light rain events (with sample sizes of about 5000 gates each) were analyzed and show similar results for all measurements (not shown). The σDP) values from the 12 cases ranged from 1.8° to 2.9° (average of 2.4°), with dispersions ranging from 0.5° to 1.0° (with an average of 0.6°). The values are dependent upon the case and dataset analyzed. Collectively, these analyses show that KPOL DP measurements are comparable to the CSU–CHILL and S-Pol radars and are of sufficient quality for algorithm development.

An additional analysis of KDP accuracy for self-consistency calibration is also performed. As discussed in section 3b(1), the self-consistency calibration technique compares processor (or user)-determined KDP with theoretical estimates of KDP (as determined by a consistency relationship). Integrating KDP over a large space–time domain substantially reduces the inherent noisiness of point KDP measurements, thereby allowing lighter rains with relatively low KDP to be acceptable for self-consistency calibration of ZH. Following Ryzhkov et al. (2005), to obtain a consistency-based reflectivity bias (ZBIAS) within 1 dB, the area–time integral of measured KDP should be estimated within 20% accuracy. The KDP measurements and their standard deviation were analyzed from five KPOL rain cases (Table 4). These are the same cases studied for QC and self-consistency calibration and are discussed in detail in later sections. To determine the accuracy or standard deviation of KDP, we used the expression from Balakrishnan and Zrnic (1989) and Carey et al. (2000),
i1520-0426-28-2-181-e3
where σDP) is the standard deviation of the total differential phase, N is the number of range gates used in KDP calculations, and Δr is the range gate spacing. The length scale for KPOL KDP calculations is 5 km and the gate spacing is 0.2 km; therefore, a 25-gate filter is used for each KDP calculation.

To avoid adverse effects from nonuniform beam filling, data were selected within specified range and azimuth boundaries containing continuous echo. Nonuniform beam filling may cause perturbations in ΦDP (Ryzhkov and Zrnic 1998c; Gosset 2004), subsequently resulting in spuriously large KDP (of both signs) in regions of strongly varying precipitation gradients (Ryzhkov 2007). For the five case studies, σDP) was calculated over 25 gate blocks from all of the volume scans. The lowest σDP) observed was 2.40° from the 19 December 2006 case, and the highest was 3.42° from the 11 August 2007 case. Inserting the lowest and highest σDP) values in (3), the resulting range of σ(KDP) in the data is from 0.17° km−1 to 0.24° km−1.

As part of the calibration approach, KDP observations are averaged within each reflectivity interval, and there is an associated reduction in σ(KDP) relative to the number of statistically independent samples. The total number of KDP samples within each reflectivity interval divided by 25 (the block averaging window) provides the number of statistically independent KDP samples. As explained in Ryzhkov et al. (2005), the reduction factor in σ(KDP) resulting from the averaging is defined as the square root of the number of independent samples. The reduction factor is then applied to the σ(KDP) high and low values to determine the σ(KDP) range in each reflectivity interval. The resulting range of σ(KDP) is then compared to the maximum allowed σ(KDP) to assess data validity.

This statistical technique was applied to each reflectivity interval from Zmin (30 dBZ) to Zmax (48 dBZ) for all of the case studies. The results from the 19 December 2006 case are shown in Table 5 and are similar to the results from all five cases. For each reflectivity interval, Table 5 shows the average KDP, the number of independent KDP samples, the reduction factor in σ(KDP) (rounded down), the maximum allowed σ(KDP), and the observed σ(KDP) (after reduction from averaging). To clarify using the 30-dBZ interval in Table 5 as an example, the average KDP is 0.053° km−1. There were 43 526 total KDP samples, so the number of independent samples is 1741 (43 526/25), resulting in an approximate factor of 41 (17410.5) reduction in σ(KDP). The range for σ(KDP) is from 0.004° km−1 (0.17/41) to 0.006° km−1 (0.24/41), which is well within the maximum allowed σ(KDP) of 0.011° km−1 (20% of the average KDP). In this reflectivity interval, and in all of the intervals from all of the cases, it is shown that the observed range of σ(KDP) is below the maximum allowed σ(KDP). Because of extensive averaging, the KDP data are valid for use in the presented self-consistency calibration method (section 3b). Now that overall quality appears acceptable for application development, data QC is considered.

b. QC techniques

KPOL data are frequently contaminated by ground and sea clutter, multiple-trip echo, and considerable noise. QC algorithms based on DP measurements have shown notable success in objective identification of these and other nonprecipitation features (Ryzhkov and Zrnic 1998b; Zrnic and Ryzhkov 1999; Cifelli et al. 2002). Five KPOL case studies with widespread rainfall from 2006 to 2007 were selected to develop an operational QC algorithm for the detection and removal of nonprecipitation echo. A monthly study from July 2008 was also performed to check the DP QC algorithm in various other conditions, such as from isolated to scattered convection and light showers to periods with only nonprecipitation echo present. Because the primary focus was the detection and removal of nonprecipitation echo during rain events, the discussion concentrates on results from the five individual case studies. In the following discussion, refer to Table 1 for the description of moments and field labels.

The multiple steps of the QC algorithm for the lowest two elevation angles are displayed in flowchart form in Fig. 2. For a primary application of quantitative rainfall estimation, the QC steps are applied below the observed radar bright band and site-specific melting level of approximately 4–5 km (Schumacher and Houze 2000). In our DP QC algorithm, a new data field with the label “CZ” is created for each volume scan and contains the final precalibrated reflectivity that has been edited for suspected nonprecipitation echo. The first step in the DP QC process is automated and applied by the RVP8 processor. From the processor user’s manual (SIGMET RVP8 processor user’s manual is available from Vaisala online at http://www.vaisala.com/weather/products/rvp8.html), signal-to-noise ratio (SNR) tests (as currently configured at KPOL) are applied to the ΦDP(PH), KDP(KD), ZDR(DR), and ρHV(RH) fields to identify gates with weak or uncertain signals, and the value of these gates are set to the no-data flag. Most multiple-trip echoes fail the KPOL-configured SNR tests within the ΦDP, KDP, and ρHV fields, and are cleanly removed by the processor. The DP QC algorithm maps all of the gates containing the no-data flag within these fields to the corresponding ZH and ZDR gates, thereby eliminating almost all of the multiple-trip echoes.

The total differential phase (ΦDP) contains both the radar system phase and a cumulative phase resulting from scattering from precipitation (Gorgucci et al. 1999; Bringi and Chandrasekar 2001). The KPOL system phase has a history of variation from near 0° to just under the maximum unambiguous value of 180°. As a consequence, the ΦDP field has shown varying amounts of aliasing depending upon the data being analyzed. A gate is considered aliased if the absolute value of the phase difference between the consecutive gates exceeds 149°. All of the aliased gates are corrected by adding 180° to the existing phase value.

An additional series of QC steps to test for typical values (in rain) and noise are applied to each gate of every ray from the ρHV, KDP, and ZDR fields. The specific thresholds applied in these tests are appropriate for KPOL observations. A simple correlation threshold test is employed, wherein gates are flagged if ρHV is less than 0.8. Correlation values within rain are considerably higher (greater than 0.9) and, therefore, the ρHV threshold of 0.8 is applied to distinguish between precipitation and clutter echoes.

The KDP threshold test flags gates with values less than −2° km−1 or greater than +3° km−1. The lower KDP threshold was determined from empirical KPOL analysis of light rain under typical operating conditions. The upper KDP threshold was determined from empirical analysis of the heaviest rain at Kwajalein (ZH near 52 dBZ), wherein KDP values do not exceed 2.4° km−1 as determined from analysis of both the radar and disdrometer data. The positive end of the KDP allowed a range corresponding to a rain rate of ∼136 mm h−1 using the R(KDP) equation of Bringi and Chandrasekar (2001).

Analyses of ZDR by the reflectivity interval (post-calibration) from the lowest two elevation sweeps indicate average values approaching 1–1.25 dB for the heaviest rain, which is similar to the ZDR range computed from disdrometer observations (discussed in section 3a). For a primary application of quantitative rainfall estimation from the lowest elevations, the ZDR test flags potential suspect gates with values less than 0 or greater than 2.5 dB. The lower ZDR threshold for rain observations was based on theory from Doviak and Zrnic (1993, their Table 8.1), while the upper threshold was subjectively determined based on low-elevation KPOL observations under typical operating conditions. Although some light rain gates may be flagged because of the lower ZDR threshold, qualitative analysis of the QCed ZDR field suggests that this may be of minimal concern. A low-reflectivity threshold test is also employed, wherein ZH gates with values less than 5 dBZ are flagged. The low ZH value test is not a validity check, but it is needed as a matter of convenience because these gates are persistent in contaminating interpolated fields for rain-rate estimation.

The calculation of σDP) and subsequent threshold testing is shown in Ryzhkov and Zrnic (1998b) to be a successful test for the detection of anomalous propagation (AP)-induced ground clutter echoes. The technique is also effective for any type of ground clutter or region of low SNR, and it has been applied to KPOL data for the identification of ground clutter from structures (i.e., buildings and towers). Robust QC results (described in the following section) indicate that 15 ΦDP gates are sufficient for estimating the standard deviation. Using a running centered 15-gate sample, σDP) is computed at each range gate. If at least 5 of the 15 gates contain valid ΦDP measurements, then their σ value is assigned to the center of the radial interval; otherwise, the σ value is set to the no-data flag. When σDP) calculations are complete for a given sweep, each gate value is checked against an empirically determined threshold. If a σDP) gate either is greater than the threshold or has been set to the no-data flag, then the corresponding ZH gate is flagged. Within accumulating rain (15 dBZZH < 55 dBZ) the typically observed average σDP) from KPOL is about 3°. Choosing a multiple of four, the threshold has been set to 12° for improved identification of AP (discussed in section 2c). In developing the DP QC algorithm, the sensitivity of multiple σDP) thresholds was empirically checked. Although initially guided by theory (Ryzhkov and Zrnic 1998b), the choice of threshold in the final analysis was primarily empirical.

The final QC step maps flagged ZH gates to the corresponding gates in ρHV, ZDR, KDP, and ΦDP. The first two elevation sweeps are QCed in this manner. The ZH field is then written to CZ for inclusion in the Universal Format (UF) volume.

c. QC results

Sea clutter, ground clutter from structures, and general noise are detected and eliminated by using a combination of σDP) and ρHV thresholding. Analysis of ρHV within sea clutter reveals values that are mostly less than 0.40; however, values in the range from 0.0 to near 0.95 can occur. A similar analysis of σDP) within sea clutter shows standard deviation values ranging from 3° to 70°. This wide range of correlation and standard deviation values is expected given the varying nature of returns from ocean waves. With a ρHV threshold of 0.80 and a σDP) threshold of 12°, almost all of the sea clutter is detected. Echoes clearly identified as ground clutter from reflectivity time series analysis display typical ρHV values in the 0.4–0.95 range. More than 50% of these ground targets have ρHV values exceeding 0.80 and could easily be incorrectly identified as precipitation echoes if the correlation test was considered alone; therefore, the σDP) test is also needed. Within ground clutter, σDP) has values ranging from 10° to near 80°, with a clear majority of values greater than 40°. The combination of the correlation and standard deviation tests identifies almost all of the ground clutter gates; however, a small percentage of problem gates are not flagged by either threshold and survive the QC tests.

Figure 3 shows typical results of the RVP8 SNR tests and DP QC algorithm for the 0.4° elevation ZH field. Figures 3a,b show raw and corrected reflectivity images within a 50-km radius and indicate the effective identification of multiple-trip echoes (by the SNR tests), sea clutter, and ground clutter along the atoll perimeter (both embedded and nonembedded) in precipitation. Figures 3c,d show a full 160-km, 0.4° elevation sweep before and after the SNR tests and DP QC. Pronounced regions of multiple-trip echoes (from 220° to 250°), ground clutter, and sea clutter have been removed in addition to widespread light noise.

The percentage of gates flagged as “bad” by each of the DP QC tests is shown in Table 6. Statistics are from the first two elevation sweeps, with a range of 0–100 km and 0°–360° in azimuth, and were determined by comparison of the fields before and after DP QC. Within these elevation and range limits, we are well below the melting level and radar-observed bright band. The relatively high percentage of flagged gates for the ZDR threshold test is due to values less than 0 dB. Gates flagged in total reflectivity (ZT) includes those from the ρHV, σDP), low ZH threshold, and no-data tests from the DP fields. The ZT percentages vary significantly from case to case and are heavily influenced by flagging those gates less than 5 dBZ.

A quantitative comparison of the results from DP QC and legacy TRMM Ground Validation System (GVS) nonpolarimetric QC reveals notable differences. As discussed in Kulie et al. (1999), the GVS QC algorithm identifies nonprecipitation echo by use of height and reflectivity threshold parameters, and it has a significant weakness in removal of high-reflectivity ground clutter, especially when the clutter is near or embedded within precipitation. The strongest precipitation echoes at Kwajalein approach 52 dBZ, but ground clutter returns easily exceed this value with measurements ranging from 55 to 70 dBZ. Figure 4 shows the location of the clutter field at Kwajalein, with 1323 gates (within 50 km of KPOL) identified as frequent sources of clutter (Silberstein et al. 2008). Reflectivity gates are extracted exclusively from these clutter locations from unedited (raw) and corrected data from both DP and GVS QC algorithms for the five daily case studies. To be reasonably certain that no precipitation echo is selected, only reflectivity values ≥55 dBZ are considered to be ground clutter. Table 7 shows the gate count ≥55 dBZ from uncorrected, DP-corrected, and GVS-corrected data. The 19 December 2006 case shows that 71 gates from a total of 11 907 extracted gates have values ≥55 dBZ. DP QC has correctly identified and removed all 71 gates (100% correction); therefore, zero clutter gates remain. GVS QC has 53 remaining clutter gates ≥55 dBZ, roughly corresponding to a 25% correction. Similar results are shown for all cases. DP QC has eliminated most clutter gates, while GVS QC has a significant numbers of clutter gates remaining. In these cases, precipitation echo is widespread and ground clutter echo is mostly embedded in (or in close proximity to) precipitation echo. The DP QC tests (correlation and standard deviation of phase) detect and remove the embedded clutter, but GVS QC historically fails in this regard. In cases with partial precipitation coverage and nonembedded clutter, it is possible for marginal improvement of GVS QC performance through threshold strengthening, but it requires repetitive labor-intensive processing. In contrast, the DP QC algorithm is fully automated and provides consistent results without the necessity of parameter adjustments.

3. KPOL calibration

a. Differential reflectivity calibration

Accurate ZDR calibration is an essential first step in the determination of absolute reflectivity calibration via consistency, and it is also critical for rain-rate estimation and hydrometeor identification. The use of vertically pointing (or birdbath) observations in light rain is a favored and reliable approach to determine ZDR bias (Gorgucci et al. 1999; Hubbert et al. 2008). The KPOL datasets from years 2006 and 2007 do not contain reliable vertical profiles; therefore, an alternative calibration method was needed for retroactive application. Although there are numerous methods described in the literature (Zrnic et al. 2006; Hubbert et al. 2003; Ryzhkov et al. 2005; Bechini et al. 2008), none are relevant or easily implemented because of operational limitations, hardware constraints, or data isolation and analysis issues.

The retroactive calibration of KPOL ZDR was accomplished through bias adjustment to a disdrometer-determined ZDR reference. Over 10 000 Joss–Waldvogel (JW) disdrometer observations of ZH and ZDR from 2003 and 2004 were compiled for this reference. The disdrometer was located at the KPOL site and recorded the entire spectrum of precipitation intensities. Assumptions regarding drop size and shape relations used in the disdrometer ZDR computation are described in section 3b(1). KPOL ZDR data from 2006 and 2007 (smoothed via a boxcar application)1 were calibrated for individual rain events by applying specific offsets determined by comparison to the disdrometer reference. Before determining the proper ZDR offset, the ZH distributions were independently calibrated by the relative calibration adjustment (RCA) method [further details are available in section 3b(2) (see Silberstein et al. 2008; Marks et al. 2009)]. The ZDRZH disdrometer reference is shown in the top panel of Fig. 5 (bold line with no symbols), together with observations from the five case studies. The level of disagreement in ZDR distributions within the cases is evident, and their bias relative to the disdrometer reference is shown in the legend. Fluctuations in ZDR bias of 0.1 to 0.2 dB were common prior to electrical upgrades in early 2008. The bottom panel of Fig. 5 shows the ZDR distributions after adjustment to the reference, and the standard deviation error bars from both instruments. The KPOL standard deviations are from the 3 August 2007 case and are representative of the standard deviations from all of the cases.

Emphasis was placed on matching ZDR within the 30–40-dBZ range because this represents approximately 85%–90% of the measurements used in self-consistency calibration. While the adjusted ZDR measurements are not in perfect agreement, and fluctuations resulting from sample size limitations are noticeable especially in the upper reflectivity intervals, our analysis indicates that the agreement is sufficient to perform a robust calibration of ZH using the self-consistency technique. After ZDR offsets were determined, the RCA-adjusted ZH values were no longer used. The self-consistency calibration of ZH (described in the following section) is completely independent of the RCA-adjusted data and method.

Measurements of ZDR in light rain with the antenna vertically pointed (at a 90° elevation angle) commenced in March 2008 and have continued through 2009. Results consistently show that the ZDR values are too high (“hot”) by approximately 1.0 dB. Electrical upgrades and calibration efforts resulted in the ZDR bias change from 2007 to 2008. Figure 6 displays vertical profile measurements from 25 September 2008 during a shallow light rain event. The vertical profile of mean ZDR (top right panel) shows bias of approximately +1 dB near the 3.0-km level. The mean ρHV values near 0.99 are indicative of sampling in the rain medium (lower left panel). A 2.8-km mean ZDR distribution by azimuth (bottom right panel) shows the periodic nature of the direction-dependent measurements, which is an expected structure resulting from variability in the ground clutter response from sidelobes with antenna rotation in the vertical (Gorgucci et al. 1999). Here, ZDR is averaged from the full azimuth cycle of 360°, over which 1023 samples per azimuth are obtained. For comparison of the birdbath and disdrometer reference methods, the mean birdbath-adjusted ZDR and standard deviation (by reflectivity interval) for data nearly concurrent with the 25 September 2008 case are plotted in the bottom panel of Fig. 5 (bold dashed line with smallest endcaps). For this case, the mean ZDR values between the two methods are very comparable, with slightly larger standard deviations for the birdbath case.

b. Self-consistency calibration: Methodology and results

1) Methodology

Polarimetric properties of the rain medium can be used to determine the absolute calibration of a radar system. Techniques used to capitalize on these consistency relations range from the comparison of rainfall rates derived from power and phase measurements (Gorgucci et al. 1992) to the comparison of the observed and estimated differential propagation phase (Goddard et al. 1994; Vivekanandan et al. 2003; Ryzhkov et al. 2005, and others). The self-consistency of ZH, ZDR, and KDP measurements was quantified by Scarchilli et al. (1996) and Gorgucci et al. (1999) using a gamma distribution model. The majority of these self-consistency calibration techniques have a common necessity of heavy rain rates (greater than 50 mm h−1) for significant phase accumulation at S band over the range profile. Ryzhkov et al. (2005) suggested a methodology for determining absolute reflectivity bias (ZBIAS) from the self-consistency relation that did not require heavy rainfall at S band. This methodology compared area–time integrals of measured (processor or user determined) KDP and estimated (theoretical) KDP as a function of ZH and ZDR. The ZBIAS was then quantified as the adjustment in ZH needed for the integrals to agree. This KDP-based method was chosen for application to KPOL data because of the predominant nature of light rain events.

The precipitation at Kwajalein is dominated by systems that form in the intertropical convergence zone (ITCZ), as well as shallow (less than 5 km) “warm rain” clouds (Schumacher and Houze 2000; Wolff et al. 2005), and it is ideal for self-consistency calibration because of this lighter rain regime. To apply the area integration methodology to KPOL data, DSD measurements from Kwajalein were required to derive a consistency equation between ZH, ZDR, and KDP. Using simulated DSD, Vivekanandan et al. (2003) derived a relationship where KDP is expressed as a function of ZH and ZDR. In our study, we derived a similar relation using actual disdrometer observations. A JW disdrometer sited at Kwajalein from May through December 2003 provided 8779 one-minute resolution DSD measurements (within the 30–48-dBZ interval) to regress the following relation between the variables:
i1520-0426-28-2-181-e4
The polarimetric radar parameters of ZH, ZDR, and KDP were calculated for each minute of DSD observations for an S-band radar (10.7 cm) and a temperature of 20°C, as shown in Tokay et al. (2002). For drop shape, the mean axis ratios offered by Andsager et al. (1999) were adopted for drops less than 4 mm in diameter and equilibrium drop shapes (Beard and Chuang 1987) for larger drops. For the fall velocity, we adopted the terminal fall velocity drop diameter relation given by Beard (1976). The coefficient and exponents were derived via a linear least squares fit regression (A = 0.177 37 × 10−4, b = 0.9926, and c = −0.5138) with ZH (mm6 m−3), ZDR (dB), and KDP (° km−1).
Following the Ryzhkov et al. (2005) method, we matched the measured KDP and estimated KDP (ZH, ZDR) by adjusting ZH by an amount (dB) considered as the ZBIAS. A practical approach to accomplish this is to divide the data collected from an entire spatial/temporal domain into 1-dB increments of radar reflectivity and compute average values of KDP(Z) and ZDR(Z) within each 1-dB interval of Z between Zmin(30 dBZ) and Zmax(48 dBZ). The ZBIAS is then determined by matching the summations
i1520-0426-28-2-181-e5
and
i1520-0426-28-2-181-e6
where n(Z) is the number of gates within each 1-dB interval. The initial estimated ZBIAS is determined from Vivekanandan et al. (2003) by
i1520-0426-28-2-181-e7
The initial ZBIAS is applied to the reflectivity field, and Eqs. (5), (6), and (7) are then recomputed to determine ΔZBIAS [from Eq. (7)]. If the resulting ΔZBIAS is greater than 0.1 dB, it is again applied to the reflectivity field. The final ZBIAS is the sum of the initial and iterated ΔZBIAS. Iteration is needed because we are subsampling the data in a ZH range, and yet we are adjusting ZH as part of the procedure. As a result, we effectively “shift” the sample of (ZH, ZDR, KDP) triplets being used in the procedure as we adjust ZH in each pass. One or two iterations are needed to force the agreement of (5) and (6), thereby reducing the ΔZBIAS to 0.1 dB. The final ZBIAS value represents the absolute ZH calibration adjustment needed for consistency between the polarimetric variables. The same cases analyzed for QC and ZDR calibration were examined for self-consistency calibration.

2) Results

As a basis for evaluation, the self-consistency results are compared against those from the independent non-DP RCA technique (Silberstein et al. 2008).2 The RCA uses a frequency distribution of reflectivity values from persistent ground clutter areas from every volume scan to monitor hourly and daily radar sensitivity changes relative to an established baseline. A practical application of the RCA technique to KPOL data revealed a dramatic improvement in data stability as evidenced by reflectivity comparisons with the TRMM precipitation radar (PR). Although the RCA provides a relative calibration, corrected KPOL reflectivity matched the PR to within ±1 dB on a monthly and yearly basis (Marks et al. 2009; Wang and Wolff 2009). Table 8 shows self-consistency calibration results as compared to the RCA approach and the absolute value of their difference. From the case studies analyzed, there is agreement between self-consistency and RCA to within ±1 dB. In four cases, the agreement is within 0.5 dB. These results are similar to Ryzhkov et al. (2005) upon comparison of corrected reflectivity with independent measurements. Illingworth and Blackman (2002) and Vivekanandan et al. (2003) have also determined that the accuracy of generally similar self-consistency calibration can be as good as 0.5–1 dB as evaluated through independent comparison. The KPOL results are consistent with previous calibration studies and provide confidence in the self-consistency method.

The consistency relationship given by (4) was derived from disdrometer observations at Kwajalein and, therefore, the relationship can serve as an empirical reference for verification of the self-consistency method after bias correction. Figure 7 shows comparisons between average KDP measurements (after ZBIAS correction) and those calculated from self-consistency [KDP (ZH, ZDR)]. There is reasonable agreement between the profiles (with the 11 August 2007 and 23 November 2007 cases as exceptions). A noticeable disagreement in profiles is apparent at both lower and upper ends of the reflectivity range. From approximately 30 to 35 dBZ, RVP8-calculated KDP is higher than consistency theory (ZH, ZDR empirical reference). This could be due to difficulty in extracting the true KDP signal (less than 0.1° km−1) from the embedded noise field despite substantial sample size and extensive averaging. The agreement is best within the 35–43-dBZ range, which is attributed to a stronger KDP signal and sufficient sample sizes. In reflectivity intervals greater than 43 dBZ, the radar-measured KDP falls lower than the reference in all cases. The number of independent KDP samples in reflectivity intervals from 43 to 48 dBZ is significantly lower than in the other intervals (<500 from the 19 December 2006 case; see Table 5). Probability distribution functions show that in all cases, approximately 95% of the KDP values within the distribution are accounted for within the 30–43-dBZ range. This result is not surprising because of the predominant occurrence of lower reflectivity precipitation at Kwajalein. These calibration results are obviously weighted with the majority of the samples; therefore, not much significance can be placed on the results from the higher reflectivity intervals.

Other explanations for disagreement in profiles at the lower and upper ends of the reflectivity range could be related to possible bias in the disdrometer-derived consistency equation and the effects of processor filtering of differential phase for KDP calculation. The relatively poor agreement in the 11 August 2007 and 23 November 2007 cases is likely related to the nature of the precipitation itself. As compared to the other cases, there is significantly more convection present and the echo shields display less of a uniform coverage pattern. This self-consistency method does not appear to be applicable to cases with numerous convective cells or scattered showers. The most favorable results are from cases with uniform, widespread, light rain shields. This finding is consistent with either 1) the calibration bias [Eq. (4)] being tuned to lighter rain DSDs (versus more convective, heavier rain DSDs) and/or 2) challenges in estimating KDP in small, isolated convective cells. The calibration results presented in Table 8 and Fig. 7 provide further confirmation of the Ryzhkov et al. (2005) method and show that an absolute bias adjustment to ZH can be determined by matching KDP profiles in relatively light rain, provided a local consistency relationship is available.

4. Summary and discussion

The development and adaptation of algorithms for QC and reflectivity calibration have been initiated in an oceanic environment with DP observations from KPOL. Presented are algorithms for DP QC and absolute reflectivity calibration using polarimetric properties of the rain medium. Application of the DP QC algorithm has shown to be robust with superior results compared to the TRMM GV (nonpolarimetric) QC algorithm that employs height and reflectivity thresholds. The ability to detect and remove ground and sea clutter embedded in precipitation echo is a distinct advantage of the DP algorithm. Through the application of thresholding tests for the correlation and standard deviation of differential phase, almost all clutter-type returns are identified and removed. In contrast, the TRMM GV algorithm can remove ground clutter only when not embedded in precipitation and can be a labor-intensive process. In addition, the RVP8 processor correctly identifies and removes multiple-trip echoes through automated SNR power tests (as currently configured at KPOL), a successful result to which the DP QC algorithm takes full advantage.

A technique for determining retroactive ZDR calibration through the analysis of combined ZDR and ZH observations was developed and applied to KPOL data. This application adjusts ZDR observations to match a disdrometer distribution when vertical profile measurements are not available. By this technique, uncertainty has been mitigated in ZDR data from significant rainfall events in 2006 and 2007 and has allowed the application of self-consistency reflectivity calibration.

A phase-based self-consistency approach used to determine absolute reflectivity calibration using properties of the rain medium in light rain has been tested with KPOL data from five case studies and found to provide good results (within ±1.0 dB) as compared to the independent RCA method. The approach follows the work of Ryzhkov et al. (2005) where KDP data from light rain events are integrated and compared against a consistency equation derived from disdrometer data at Kwajalein. In lower reflectivity intervals (30–35 dBZ), the observed KDP measurements indicate a high bias relative to the disdrometer-based reference, possibly resulting from difficulty in extracting the true KDP signal. In midreflectivity intervals (35–43 dBZ), there is reasonable agreement between observed and consistency-derived KDP profiles. Differences may be related to possible bias in the disdrometer-derived consistency equation and the assumptions from which it was derived. The results indicate that the method can be successfully applied to lighter precipitation regimes. The most favorable results were found in cases with widespread, uniform, light rain shields.

The Ryzhkov et al. (2005) consistency calibration method was developed with polarimetric observations from central Oklahoma. In our study, we present another careful test of Ryzhkov et al. (2005) from a very different meteorological regime. The encouraging results increase confidence that the technique might have a future in near-real-time operations for at least TRMM and GPM GV with WSR-88D radars from many environments (Morris and Schwaller 2009), but that the application and resulting interpretation may need expert user oversight. It is not clear at this time if future baseline WSR-88D DP data made available to the community by the National Oceanic and Atmospheric Administration (NOAA) will have sufficient calibration for research applications. For certain, NASA’s PMM GV programs will require continued verification of WSR-88D calibration using all available means, and the results of this study suggest that the consistency method of Ryzhkov et al. (2005), and possibly the RCA method of Silberstein et al. (2008), may be viable options for select radars at a minimum.

DP radars will certainly be a vital tool for GPM validation because of their applications to rainfall microphysical retrievals (Chandrasekar et al. 2008). Through the retrieval of DSD parameters relating drop size and shape, rainfall estimation, and hydrometeor identification, DP radars can provide validation of parameterized microphysical properties. The ability to provide consistent and long-term QCed and calibrated ground-based DP measurements will prove essential for calibration of the core GPM satellite and for development of physically based passive microwave radiometer algorithms.

Acknowledgments

This research is supported by NASA Grant NNG07EJ50C. The authors thank Dr. Ramesh Kakar (NASA Headquarters), Dr. Arthur Hou (GPM Project Scientist, NASA/GSFC), Dr. Scott Braun (TRMM Project Scientist, NASA/GSFC), and Dr. Mathew Schwaller (GPM GV Program Manager, NASA/GSFC) for their support of this effort. Appreciation is extended to David Silberstein for numerous helpful discussions, and to the TRMM Satellite Validation Office staff, including Bart Kelley, Jason Pippitt, David Makofski, and Jianxin Wang. CSU–CHILL data were provided by Patrick Kennedy of Colorado State University. NCAR S-Pol data were provided by the NCAR ATD. We thank the staff of Atmospheric Technology Services Company for providing KPOL data.

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Fig. 1.
Fig. 1.

The location of Kwajalein Atoll (from Wolff et al. 2005). The KPOL S-band radar is located on Kwajalein Atoll at the center of the image (8.7°N, 167.7°E). Rain gauge locations from the KWA network are shown (black squares).

Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHA1462.1

Fig. 2.
Fig. 2.

KPOL quality control algorithm flowchart for the first two elevation angles. See text for explanation.

Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHA1462.1

Fig. 3.
Fig. 3.

Examples showing persistent ground clutter and multiple-trip echoes (a) in raw KPOL data (0638 UTC 5 Apr 2006 zoomed image with 50-km range ring), and (b) removal of the nonprecipitation echoes by the RVP8 processor SNR tests and the DP QC algorithm. (c) A raw 0.4° elevation sweep shows significant multiple-trip echoes (southwest of KPOL, 20–160-km range), ground and sea clutter, and typical noise (from 0428 UTC 5 Apr 2006). (d) The DP QC and processor corrected field shows dramatic improvement. Range rings are at 50-km intervals.

Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHA1462.1

Fig. 4.
Fig. 4.

Map of the clutter field at Kwajalein. Range rings are drawn at 10-km intervals from the radar site. (From Silberstein et al. 2008)

Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHA1462.1

Fig. 5.
Fig. 5.

Distribution of average ZDR measurements by reflectivity interval. (top) The unadjusted ZDR curves show the bias in five case studies relative to the JW disdrometer ZDR reference (bold, no-symbol line). Biases are shown in the legend. (bottom) The ZDR distributions bias adjusted to the disdrometer reference. The ZDR standard deviation error bars for the disdrometer (longest endcaps) and KPOL (midsized endcaps) are very similar in this data range. The KPOL standard deviations are from the 3 Aug 2007 case and are representative of the standard deviations from all five case studies. For comparison, the 25 Sep 2008 (birdbath adjustment method) average ZDR and standard deviations are shown by the heavy dashed line and smallest endcaps (reference Fig. 6 and associated text); ZH distributions have been calibration corrected via the independent RCA method.

Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHA1462.1

Fig. 6.
Fig. 6.

Measurements of (top left) reflectivity with height, (top right) mean ZDR with height, (bottom left) correlation with height, and (bottom right) mean ZDR measurements with azimuth for a shallow light rain event at Kwajalein from 25 Sep 2008. The correlation profile indicates sampling in the rain medium near 3.0-km height. The azimuth measurements (bottom right) show the influence of directional-dependent response. The mean ZDR bias of +0.97 dB (heavy dashed lined) was determined over the full azimuth cycle. The dash–dot lines represent one standard deviation.

Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHA1462.1

Fig. 7.
Fig. 7.

Comparison of radar processor determined KDP measurements and computed KDP measurements from self-consistency theory. The self-consistency relationship was developed from disdrometer measurements at Kwajalein. Results are shown from each of the five case studies.

Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHA1462.1

Table 1.

KPOL basic characteristics, moments recorded, and field descriptions.

Table 1.
Table 2.

Task configuration of the KPOL radar. Columns are task name, radar polarization, elevation angles (°), and pulse repetition frequency (PRF). Ground validation volume scans initially alternated between A and B (GVVOL_A and GVVOL_B), with one surveillance scan (Surv_TRMM) between volume scan sets. There were 10 volume scans per hour (five A scans and five B scans). The alternating scanning was replaced with a single 17-elevation volume scan (GVVOL) with six volume scans per hour in October 2008.

Table 2.
Table 3.

Empirical investigation of relative DP radar performance in light rain from the CSU–CHILL, S-Pol, and KPOL radars. Shown are the median values for ZH, ρHV, and KDP (with standard deviation in parenthesis), the average deviation of ZDR from its mean value [Eq. (1)], and the average absolute deviation of ZDR [AAD ZDR (Eq. 2)] representing error measurement of the ZDR field. The median standard deviation of the measured differential phase σDP) (with associated dispersion) provides an indication of phase data quality for use in DP applications. The higher value for KPOL σDP) is within the acceptable boundaries for DP applications. Considering similar statistical sample sizes (No. of gates), measurements from KPOL in light rain are comparable to those from established by CSU–CHILL and S-Pol polarimetric radars.

Table 3.
Table 4.

Five KPOL case studies and time periods selected for analysis of KDP, and applications of quality control and self-consistency calibration.

Table 4.
Table 5.

Reflectivity interval statistics to determine KDP data validity from the 19 Dec 2006 case study. Shown are reflectivity interval, average KDP within the interval, number of independent KDP samples, reduction factor (rounded down) in KDP standard error resulting from averaging, maximum allowed standard deviation of KDP, and the standard deviation range of KDP within the interval.

Table 5.
Table 6.

DP QC algorithm results for each of the case studies. Statistics represent the maximum percentage of gates flagged as “bad” or “noise” by the individual tests from the first two elevation sweeps within each volume scan. Statistics are from the rainfall estimation range of 0–100 km and 0°–360° in azimuth, and were determined by comparing the final QC field with the initial non-QC field.

Table 6.
Table 7.

Comparison of DP QC and nonpolarimetric TRMM GVS QC results with respect to ground clutter detection. Raw reflectivity data were extracted from locations with frequent ground clutter echoes. The gate count represents the remaining gates considered to be ground clutter after QC is applied. For this study, gates ≥55 dBZ are considered ground clutter. DP QC shows superior performance as compared to the nonpolarimetric (TRMM GVS) QC as evidenced by the low gate counts.

Table 7.
Table 8.

Self-consistency-derived calibration adjustments as compared with the independent RCA approach, and the absolute value of their difference. Shown is the cumulative number of KDP samples compared (measured and derived via consistency) from the reflectivity intervals in the Zmin (30 dBZ) to Zmax (48 dBZ) range.

Table 8.

1

Each ZDR gate has been smoothed by a “boxcar” application. A smoothed gate is defined as the average ZDR value from five gates (i.e., a specific gate and the four surrounding gates). The four surrounding gates are defined as 1) the next gate in the same ray, 2) the previous gate in the same ray, 3) the corresponding gate from the next ray, and 4) the corresponding gate from the previous ray. More information can be obtained from Bringi and Thurai (2008).

2

The RCA-adjusted ZH reflectivity values are not used in any way in the self-consistency calibration method. The RCA is a completely independent statistical calibration approach.

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  • Fig. 1.

    The location of Kwajalein Atoll (from Wolff et al. 2005). The KPOL S-band radar is located on Kwajalein Atoll at the center of the image (8.7°N, 167.7°E). Rain gauge locations from the KWA network are shown (black squares).

  • Fig. 2.

    KPOL quality control algorithm flowchart for the first two elevation angles. See text for explanation.

  • Fig. 3.

    Examples showing persistent ground clutter and multiple-trip echoes (a) in raw KPOL data (0638 UTC 5 Apr 2006 zoomed image with 50-km range ring), and (b) removal of the nonprecipitation echoes by the RVP8 processor SNR tests and the DP QC algorithm. (c) A raw 0.4° elevation sweep shows significant multiple-trip echoes (southwest of KPOL, 20–160-km range), ground and sea clutter, and typical noise (from 0428 UTC 5 Apr 2006). (d) The DP QC and processor corrected field shows dramatic improvement. Range rings are at 50-km intervals.

  • Fig. 4.

    Map of the clutter field at Kwajalein. Range rings are drawn at 10-km intervals from the radar site. (From Silberstein et al. 2008)

  • Fig. 5.

    Distribution of average ZDR measurements by reflectivity interval. (top) The unadjusted ZDR curves show the bias in five case studies relative to the JW disdrometer ZDR reference (bold, no-symbol line). Biases are shown in the legend. (bottom) The ZDR distributions bias adjusted to the disdrometer reference. The ZDR standard deviation error bars for the disdrometer (longest endcaps) and KPOL (midsized endcaps) are very similar in this data range. The KPOL standard deviations are from the 3 Aug 2007 case and are representative of the standard deviations from all five case studies. For comparison, the 25 Sep 2008 (birdbath adjustment method) average ZDR and standard deviations are shown by the heavy dashed line and smallest endcaps (reference Fig. 6 and associated text); ZH distributions have been calibration corrected via the independent RCA method.

  • Fig. 6.

    Measurements of (top left) reflectivity with height, (top right) mean ZDR with height, (bottom left) correlation with height, and (bottom right) mean ZDR measurements with azimuth for a shallow light rain event at Kwajalein from 25 Sep 2008. The correlation profile indicates sampling in the rain medium near 3.0-km height. The azimuth measurements (bottom right) show the influence of directional-dependent response. The mean ZDR bias of +0.97 dB (heavy dashed lined) was determined over the full azimuth cycle. The dash–dot lines represent one standard deviation.

  • Fig. 7.

    Comparison of radar processor determined KDP measurements and computed KDP measurements from self-consistency theory. The self-consistency relationship was developed from disdrometer measurements at Kwajalein. Results are shown from each of the five case studies.

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